Nanosheet surface roughness and profile metrology

Abstract

An inspection system includes a controller including a memory that maintains program instructions and one or more processors configured to execute the program instructions. The program instructions cause the one or more processors to generate a geometric model of a structure of a sample, generate an optical response function model of the structure of the sample to illumination based at least in part on the geometric model, receive measurement data from a detector, a parametric substructure model is generated based at least on the optical response function model and the measurement data and one or more parameters of the structure are extracted based on the measurement data.

Description

Technical Field

[0001] The present disclosure generally relates to spectroscopic metrology, and more particularly, to spectroscopic metrology of nanosheets. Background Art

[0002] The evolution of semiconductor manufacturing has placed increasing demands on yield management and particularly on metrology and inspection systems. Critical dimensions are continuously shrinking while wafer sizes are increasing. Economics drive the industry to reduce the time required to achieve high yield, high value production. Minimizing the total time from detecting a yield problem to fixing it determines the return on investment for semiconductor manufacturers.

[0003] Metrology can be used to make various measurements on, for example, semiconductor wafers or photomasks during semiconductor manufacturing. Metrology tools can be used to measure structural and material properties associated with various semiconductor manufacturing processes. For example, a metrology tool can measure material composition or can measure dimensional properties of structures and films, such as film thickness, critical dimension (CD) of a structure, or overlay. These measurements are used to facilitate process control and / or throughput efficiency during semiconductor die fabrication.

[0004] As semiconductor device pattern sizes continue to shrink, smaller metrology targets are typically required. Additionally, the requirements for measurement accuracy and matching actual device characteristics increase the need for device-class targets and measurements in and even on the die. Thus, it would be advantageous to provide devices, systems, and methods that address the above disadvantages. Summary of the Invention

[0005] According to one or more embodiments of the present disclosure, an inspection system is described. The inspection system includes a controller. The controller includes a memory that maintains program instructions. The controller includes one or more processors configured to execute the program instructions. The program instructions cause the one or more processors to generate a geometric model of the structure of a sample. The structure includes a nanosheet profile having surface roughness. The geometric model approximates the surface roughness. The program instructions cause the one or more processors to generate an optical response function model of the illumination of the structure of the sample based at least in part on the geometric model. The optical response function model simulates the optical response of the nanosheet profile having the surface roughness to the illumination. The program instructions cause the one or more processors to receive measurement data from a detector. The measurement data includes a measured spectrum of the structure detected by the detector. The program instructions cause the one or more processors to generate a parametric substructure model based at least on the optical response function model and the measurement data. The program instructions cause the one or more processors to extract one or more parameters of the structure based on the measurement data.

[0006] In some embodiments, the geometric model approximates the surface roughness of the nanosheet profile by representing the nanosheet profile as a homogeneous layer and a rough layer. The rough layer is a coating material surrounding the homogeneous layer.

[0007] In some embodiments, the one or more parameters include the standard deviation of the surface roughness.

[0008] In some embodiments, the homogeneous layer includes a material. The homogeneous layer includes one or more dispersion parameters associated with the material; wherein the one or more dispersion parameters include the refractive index (n) and the extinction coefficient (k).

[0009] In some embodiments, the rough layer includes one or more dispersion parameters determined using the effective medium approximation. The one or more dispersion parameters include the refractive index (n) and the extinction coefficient (k).

[0010] In some embodiments, the rough layer is a mixture of a first material and a second material in a certain ratio; wherein the first material is different from the second material.

[0011] In some embodiments, the ratio is a fixed ratio.

[0012] In some embodiments, the program instructions cause the one or more processors to make the ratio float.

[0013] In some embodiments, the rough layer is isotropic; wherein the surface roughness is anisotropic.

[0014] In some embodiments, the geometric model approximates the surface roughness by building blocks. The height of the building blocks varies along a direction.

[0015] In some embodiments, the height of the building blocks is defined by a plurality of segments.

[0016] In some embodiments, each of the plurality of segments includes a segment height at a critical dimension along the direction.

[0017] In some embodiments, the segment height is defined as either a fixed segment height or a percentage segment height.

[0018] In some embodiments, the critical dimension is defined as either a fixed critical dimension from the edge or a percentage critical dimension.

[0019] In some embodiments, the plurality of segments are plates; wherein the building blocks include a stepped shape.

[0020] In some embodiments, the program instructions cause the one or more processors to adjust the resolution of the height of the building block by adjusting the number of the plurality of segments.

[0021] In some embodiments, the height of the building block is defined by one or more polynomial functions.

[0022] In some embodiments, the nanosheet profile includes a first surface and a second surface. The first surface is opposite to the second surface; wherein the first surface is defined by a first polynomial function. The second surface is defined by a second polynomial function. The height of the building block is defined by the first polynomial function and the second polynomial function.

[0023] In some embodiments, the first polynomial function is different from the second polynomial function.

[0024] In some embodiments, the one or more parameters include roughness amplitude and correlation length.

[0025] In some embodiments, the one or more parameters include height profiles at a plurality of positions along the direction.

[0026] In some embodiments, the inspection system includes a user input source. The program instructions cause the one or more processors to receive user input from the user input source. The one or more processors generate the geometric model at least in part based on the user input.

[0027] In some embodiments, the inspection system includes an optical imaging subsystem. The optical imaging subsystem includes an illumination source and the detector. The illumination source generates the illumination. The detector is communicatively coupled to the controller.

[0028] In some embodiments, the optical imaging subsystem includes at least one of a spectroscopic ellipsometer, a reflectometer, a small-angle x-ray scattering meter, a scanning electron microscope, or a transmission electron microscope.

[0029] In some embodiments, the nanosheet profile includes at least one of a rhombic cross-section, an elliptical cross-section, a triangular cross-section, a rectangular cross-section, or a trapezoidal cross-section.

[0030] In some embodiments, the structure is a gate-all-around (GAA) transistor.

[0031] In some embodiments, the nanosheet profile includes a thickness of 5 nanometers or less.

[0032] In some embodiments, the program instructions cause the one or more processors to generate the optical response function model using rigorous coupled-wave analysis (RCWA).

[0033] In some embodiments, the parametric substructure model is a neural network model trained using the optical response function model and the measurement data.

[0034] According to one or more embodiments of the present disclosure, a method is described. The method includes generating a geometric model of the structure of a sample. The structure includes a nanosheet profile having surface roughness. The geometric model approximately calculates the surface roughness. The method includes generating, at least in part based on the geometric model, an optical response function model of the structure of the sample to illumination. The optical response function model simulates the optical response of the nanosheet profile having the surface roughness to the illumination. The method includes receiving measurement data from a detector. The measurement data includes a measurement spectrum of the structure detected by the detector. The method includes generating a parametric substructure model based at least on the optical response function model and the measurement data. The method includes extracting one or more parameters of the structure based on the measurement data.

[0035] In some embodiments, the geometric model approximately calculates the surface roughness by representing the nanosheet profile as a homogeneous layer and a rough layer. The rough layer is a coating material surrounding the homogeneous layer.

[0036] In some embodiments, the rough layer includes one or more dispersion parameters determined using an effective medium approximation. The one or more dispersion parameters include a refractive index (n) and an extinction coefficient (k).

[0037] In some embodiments, the rough layer is a mixture of a first material and a second material at a certain ratio. The first material is different from the second material.

[0038] In some embodiments, the rough layer is isotropic. The surface roughness is anisotropic.

[0039] In some embodiments, the geometric model approximately calculates the surface roughness by building blocks. The height of the building blocks varies along a direction.

[0040] In some embodiments, the height of the building blocks is defined by a plurality of segments. Each of the plurality of segments includes a segment height at a critical dimension along the direction.

[0041] In some embodiments, the segment height is defined as one of a fixed segment height or a percentage segment height. The critical dimension is defined as one of a fixed critical dimension from an edge or a percentage critical dimension.

[0042] In some embodiments, the height of the building blocks is defined by one or more polynomial functions.

[0043] In some embodiments, the nanoplate profile includes a first surface and a second surface. The first surface is opposite to the second surface. The first surface is defined by a first polynomial function. The second surface is defined by a second polynomial function. The height of the building block is defined by the first polynomial function and the second polynomial function.

[0044] In some embodiments, the one or more parameters include at least one of the standard deviation of the surface roughness, the roughness amplitude and the correlation length, and the height profile.

[0045] It should be understood that the above general description and the following detailed description are for illustration and explanation only and do not necessarily limit the present invention. The drawings incorporated in this specification and constituting a part of this specification illustrate embodiments of the invention and, together with the general description, are used to explain the principles of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Those skilled in the art can preferably understand several advantages of the present disclosure by referring to the accompanying drawings, in which:

[0047] Figure 1A A block diagram illustrating an inspection system according to one or more embodiments of the present disclosure.

[0048] Figure 1B A simplified schematic diagram illustrating an inspection system suitable for optical measurement according to one or more embodiments of the present disclosure.

[0049] Figure 1C A simplified schematic diagram illustrating an inspection system suitable for optical measurement according to one or more embodiments of the present disclosure.

[0050] Figure 2A A view illustrating the structure of a sample including one or more nanoplates according to one or more embodiments of the present disclosure.

[0051] Figure 2B An illustration of a nanoplate having surface roughness according to one or more embodiments of the present disclosure.

[0052] Figure 3 A block diagram depicting a model construction and analysis engine according to one or more embodiments of the present disclosure.

[0053] Figure 4A A view depicting the profile of an effective medium approximation (EMA) model according to one or more embodiments of the present disclosure.

[0054] Figures 4B to 4C A plot depicting the dispersion parameters of the EMA model profile according to one or more embodiments of the present disclosure.

[0055] Figure 5ADepict a building block including segments according to one or more embodiments of the present disclosure.

[0056] Figure 5B Depict a building block including a surface bounded by a polynomial function according to one or more embodiments of the present disclosure.

[0057] Figure 6 Depict a flowchart of a method according to one or more embodiments of the present disclosure. Detailed Description

[0058] Reference will now be made in detail to the subject matter illustrated in the accompanying drawings. The present disclosure has been particularly shown and described with respect to particular embodiments and specific features thereof. The embodiments set forth herein are to be considered illustrative rather than limiting. Those skilled in the art will readily appreciate that various changes and modifications can be made to the form and details without departing from the spirit and scope of the present disclosure.

[0059] As the design of both the composite materials and geometries (e.g., size, shape, material interfaces, etc.) of the target structures for next-generation thin FinFETs or fully surrounding gate FETs becomes increasingly complex, current methods cannot accommodate all of the required measurement steps to ensure high measurement quality and thus high yield.

[0060] Nanostructures can include surface roughness. The surface roughness can introduce anisotropy into the nanostructures. In the fully surrounding gate (GAA) semiconductor manufacturing process, the surface roughness of the nanosheets is critical to the final device performance. As the nanosheet thickness shrinks below 5 nm and the gate length approaches 10 nm, the atomic-scale variations due to surface roughness must be monitored, controlled, and minimized because they have a great impact on the performance variations from one nanosheet to another.

[0061] Methods for nanoscale surface tomography of surface roughness include transmission electron microscopy (TEM) and atomic force microscopy (AFM). However, TEM and AFM have several drawbacks. TEM is a destructive technique. TEM is not suitable for in-line metrology. TEM requires the preparation of a surface-protected cross-section and the deposition of thin film materials, such as applying a coating on the surface. Sample preparation from GAA wafers is very time-consuming. TEM requires image analysis to extract roughness parameters. TEM cannot ensure the protection of the original surface. In other words, the measurement itself modifies the target parameter. TEM can introduce potential inaccuracies and artifacts due to sample preparation prior to measurement. Similarly, AFM is destructive and can damage the sample. AFM is a contact measurement. The sample can be degraded due to the tip contact of AFM. The scan speed of AFM is another limitation. AFM requires a typical scan of several minutes, making AFM regarded as ultra-low throughput. AFM can introduce artifacts unless high-quality tips are used. AFM can also introduce image distortion due to lateral forces. AFM has difficulty in probing cliffs, sidewalls, and overhanging arms. AFM is also not suitable for any in-line measurement.

[0062] Metrology techniques (e.g., spectroscopy- or scatterometry-based metrology) provide alternative methods for nanoscale surface tomography. Metrology techniques characterize parameters of semiconductor wafers during the manufacturing process. Specifically, light is directed onto periodic gratings formed in semiconductor wafers. The spectrum of the reflected light is measured and analyzed to characterize grating parameters. Various parameters can be determined, such as critical dimension (CD), film thickness, optical properties and composition, overlay, lithography focus / dose, and the like. Various parameters typically require a geometric model of the underlying structure to be measured.

[0063] Metrology techniques require a great deal of prior knowledge of the relevant periodic structures. Any kind of roughness is a potential source of measurement error or uncertainty. Roughness is a source of error for periodic structures and is a parameter of concern. Nanoplate roughness results in three-dimensional nanoplate properties without periodicity. Therefore, it becomes very challenging to solve the Maxwell equations by considering a randomly rough surface. Therefore, approximation methods are preferred.

[0064] Optical scatterometry measurement data is sensitive to both the geometric features of the transistor structure and the optical properties of the underlying materials. Measuring the geometric features of the transistor structure includes surface roughness. The effect of surface roughness can be de-correlated from other contributing factors, such as the optical properties and material properties of other structures captured in the measurement.

[0065] The method involves designing and implementing a flexible surface shape of a nanosheet model that can measure sheet-specific roughness in GAA. The flexible surface shape model (also known as the surface shape building block) is an innovative and advanced rigorous coupled wave (RCWA) model. In combination with appropriate interference techniques and machine learning (ML) algorithms, the method of the present invention has demonstrated accurate and robust measurement of nanoscale surface roughness.

[0066] Methods and systems for generating a measurement model with a flexible surface shape of a nanosheet are presented herein. The flexible surface shape of the nanosheet enables the generation of a measurement model that is substantially simpler, has fewer errors, and is more accurate. Accordingly, the time to obtain useful measurement results is significantly reduced, especially when modeling nanosheet structures. The flexible surface shape of the nanosheet is used to generate a measurement model of a metrology system. The metrology system employing the measurement model is then configured to measure structural and material properties associated with the nanosheet (such as the material composition of the structure and film, dimensional properties, etc.).

[0067] The nanosheet surface profile must be monitored, controlled, and minimized because it has a significant impact on performance variations from one nanosheet to another. The actual nanosheet profile contains non-uniform sheet heights. It is necessary to be able to control the individual heights at different lateral segments within a single nanosheet building block to measure the sheet surface roughness in an optical critical dimension (CD) rigorous coupled wave (RCWA) model. The RCWA modeling building block is described using a physics-assisted machine learning method to enable nanosheet surface roughness measurement for in-fab line processes.

[0068] A metrology solution for determining nanosheet roughness and profile is described. The metrology solution is non-destructive, relatively faster, and introduces few artifacts. A specially designed optical method (such as scatterometry) equipped with appropriate algorithms and methods can be a potential candidate due to its speed advantage to allow for a higher sampling rate, non-contact mode, non-destructiveness, and avoidance of damaging the wafer. The controller accurately extracts the nanosheet surface roughness and the nanosheet surface profile from the spectral optical response.

[0069] The metrology solution includes methods and models, algorithms, a set of RCWA flexible building blocks, and / or methods and models using the EMA method. The metrology solution can be designed to address different process metrology requirements, which include but are not limited to nanosheet roughness (t standard deviation), nanosheet roughness amplitude (δ), and correlation length (Γ), and / or the nanosheet continuous height profile. Any of the metrology requirements can be selected depending on the application and use case.

[0070] Nanoplatelet approximation calculations can be modeled as anisotropic or isotropic. Isotropic EMA can model interface roughness in ellipsometry. EMA can be extended to more accurate and generalized anisotropic models because this type of roughness has a preferred orientation. The preferred orientation can be attributed to wet etching of silicon germanium (SiGe). In some embodiments, isotropic EMA includes nanoplatelets in two layers, such as a rough layer and a homogeneous layer. Alternatively, anisotropic approximation calculations can model interface roughness in ellipsometry. Anisotropic approximation calculations can be desirable due to higher accuracy. In some embodiments, anisotropic approximation calculations include nanoplatelets in one or more segments. In some embodiments, anisotropic approximation calculations include using a polynomial equation to represent the surface of the nanoplatelets.

[0071] U.S. Patent No. 10,458,912 titled "Model-based optical measurements of semiconductor structures with anisotropic dielectric permittivity", U.S. Patent No. 11,573,077 titled "Scatterometry based methods and systems for measurement of strain in semiconductor structures", U.S. Patent No. 11,036,898 titled "Measurement models of nanowire semiconductor structures based on re-useable sub-structures", U.S. Patent No. 11,555,689 titled "Measuring thin films on grating and bandgap on grating", U.S. Patent No. 11,156,548 titled "Measurement methodology of advanced nanostructures", U.S. Patent No. 10,794,U.S. Patent No. 839, U.S. Publication No. 2014 / 0297211 entitled "Statistical model-based metrology", U.S. Publication No. 2015 / 0046118 entitled "Differential methods and apparatus for metrology of semiconductor targets", U.S. Publication No. 2016 / 0109375 entitled "Measurement Of Small Box Size Targets", U.S. Publication No. 2016 / 0141193 entitled "System, method and computer program product for combining raw data from multiple metrology tools", U.S. Publication No. 2016 / 0282105 entitled "Model-Based Single Parameter Measurement", U.S. Publication No. 2014 / 0316730 entitled "On-device metrology", U.S. Publication No. 2015 / 0046118 entitled "Differential methods and apparatus for metrology of semiconductor targets", U.S. Patent No. 11,378,451 entitled "Bandgap measurements of patterned film stacks using spectroscopic metrology", and U.S. Patent No. 11,156,548 entitled "Measurement methodology of advanced nanostructures" are hereby incorporated by reference in their entireties.,

[0072] Reference is now made Figures 1A to 6 , and systems and methods for optical inspection are described in more detail in accordance with one or more embodiments of the present disclosure.

[0073] Figure 1A is a block diagram of an inspection system 100 in accordance with one or more embodiments of the present disclosure. In the field of semiconductor metrology, the inspection system 100 may include an optical imaging subsystem 102. The optical imaging subsystem 102 includes an illumination subsystem 106 that illuminates a target and a photon collection subsystem 112 that captures relevant information provided by the interaction (or lack thereof) of the illumination subsystem 106 with the target, device, or feature. The inspection system 100 also includes a controller 124 (e.g., a processing system) that analyzes the information collected using one or more algorithms.

[0074] The inspection system 100 may include any type of metrology system known in the art suitable for providing a metrology signal associated with a metrology target on a sample. The optical imaging subsystem 102 may include one or more hardware configurations. For example, the optical imaging subsystem 102 may include, but is not limited to, a spectrometer, a spectroscopic ellipsometer having one or more illumination angles, a spectroscopic ellipsometer for measuring Mueller matrix elements (e.g., using a rotating compensator), a single-wavelength ellipsometer, an angular-resolved ellipsometer (e.g., a beam-profile ellipsometer), a spectroscopic reflectometer (e.g., a broadband reflectance spectrometer), a single-wavelength reflectometer, an angular-resolved reflectometer (e.g., a beam-profile reflectometer), a pupil imaging system, a spectral imaging system, or a scatterometer (e.g., a speckle analyzer). The hardware configurations may be separated into discrete operating systems. On the other hand, one or more hardware configurations may be combined into the inspection system 100. For example, multiple metrology heads may be integrated into the inspection system 100.

[0075] In one embodiment, the inspection system 100 is configured to provide a spectral signal indicative of one or more optical properties (e.g., one or more dispersion parameters and the like) of the metrology target at one or more wavelengths. In one embodiment, the inspection system 100 includes an image-based metrology tool for measuring metrology data based on generating one or more images of the sample. In another embodiment, the inspection system 100 includes a scatter-based metrology system for measuring metrology data based on scattered (reflected, diffracted, diffusely scattered, and the like) light from the sample.

[0076] In one embodiment, the inspection system 100 includes one or more optical imaging subsystems 102 (e.g., optical imaging tools). In some embodiments, the inspection system 100 may include a single optical imaging subsystem 102 or multiple optical imaging subsystems 102 (e.g., Figure 1B , Figure 1C) When the inspection system 100 is a spectral imaging system, the multiple optical imaging subsystems 102 of the spectral imaging system may include a broadband spectroscopic ellipsometer, a spectroscopic ellipsometer with a rotating compensator, a beam profile ellipsometer, a beam profile reflectometer, a broadband reflectance spectrometer, a deep ultraviolet reflectance spectrometer, and the like. Further contemplated, the optical imaging subsystem 102 includes several optical elements in such systems, which include specific lenses, collimators, mirrors, quarter-wave plates, polarizers, detectors, cameras, apertures, and / or light sources.

[0077] One or more optical imaging subsystems 102 are configured to generate one or more images of the sample 104. For example, the optical imaging subsystem 102 may include: an illumination subsystem 106 configured to illuminate the sample 104 with illumination 108 from an illumination source 110; and a light collection subsystem 112 configured to generate an image of the sample 104 using a detector 116 in response to light (e.g., sample light 114) emitted from the sample illumination 108.

[0078] The illumination subsystem 106 includes one or more illumination sources 110. Examples of suitable light sources are white light sources, ultraviolet (UV) lasers, arc lamps or electrodeless lamps, laser sustained plasma (LSP) sources, supercontinuum sources (e.g., broadband laser sources), or shorter wavelength sources (e.g., x-ray sources), extreme UV sources, or some combination thereof.

[0079] The illumination source 110 may generate illumination 108. The illumination 108 may have only one wavelength (i.e., monochromatic light), several discrete wavelengths (i.e., polychromatic light), multiple wavelengths (i.e., broadband light), and / or sweep through wavelengths that are continuous or jump between wavelengths (i.e., tunable source or sweep source). For example, the illumination 108 may include wavelengths that vary from about 120 nm to about 3 microns. The illumination 108 may include luminance, which in some cases may be a luminance greater than about 1 W / (nm cm2 Sr). The illumination 108 may be polarization-resolved, unpolarized, or the like.

[0080] The sample 104 may include a substrate (such as a wafer or the like) formed of a semiconductor or non-semiconductor material. For example, the semiconductor or non-semiconductor material may include, but is not limited to, single-crystalline silicon, gallium arsenide, and indium phosphide. The sample 104 may further include one or more layers disposed on the substrate. For example, such layers may include, but are not limited to, photoresist, dielectric materials, conductive materials, and semi-conductive materials. Several different types of such layers are known in the art, and the term sample as used herein is intended to cover samples on which all types of such layers can be formed. The one or more layers formed on the sample may be patterned or unpatterned. For example, the sample may include multiple dies each having repeatable patterned features. The formation and processing of such material layers may ultimately result in a completed device. Several different types of devices may be formed on the sample, and the term sample as used herein is intended to cover samples on which any type of device known in the art can be fabricated.

[0081] The sample 104 may include one or more targets. A target may also be referred to as a metrology target. The targets are interrogated by the inspection system 100. The targets may include specific regions of interest having periodicity, such as gratings in memory dies. A metrology target may include multiple layers (such as films) whose thickness can be measured by the inspection system 100. The targets may include target designs placed (or already existing) on a semiconductor wafer for use (e.g., through alignment and / or overlay registration operations). Additionally, the targets may be located at multiple sites on the semiconductor wafer. For example, the targets may be located within scribe lanes (e.g., between dies) and / or within the dies themselves. In a particular embodiment, multiple targets are measured (simultaneously or at different times) by the same or multiple metrology tools.

[0082] The optical imaging subsystem 102 may use any technique known in the art to generate one or more images of the sample 104. In some embodiments, the optical imaging subsystem 102 is an optical imaging subsystem 102, where the illumination source 110 is a light source configured to generate illumination 108 in the form of light and where the photon collection subsystem 112 images the sample 104 based on light emitted from the sample 104. In some embodiments, the imaging subsystem 102 is a particle imaging subsystem 102, where the illumination source 110 is a particle source configured to generate illumination 108 in the form of particles. For example, the particle illumination 108 may be in the form of an electron beam (e-beam), an ion beam (such as a focused ion beam), or a neutral particle beam. Additionally, the photon collection subsystem 112 may image the sample 104 based on particles (such as backscattered electrons or the like) emitted from the sample 104. In some cases, the particle inspection system 100 may also image the sample 104 based on light (such as based on photoluminescence or the like) emitted from the sample 104 in response to incident particle illumination 108.

[0083] The optical imaging subsystem 102 can, but need not, measure the composition of one or more layers of a multi-layer stack (such as a planar multi-layer stack, a multi-layer grating, and the like) or one or more defects on or within a sample. Multiple targets can be measured simultaneously or sequentially by the same or multiple metrology tools. In certain embodiments, multiple targets are measured (simultaneously or at different times) by the same or multiple optical imaging subsystems 102. Data from such measurements can be combined.

[0084] The optical imaging subsystem 102 can provide various types of measurements related to semiconductor manufacturing. For example, the optical imaging subsystem 102 can provide one or more metrology metrics for one or more metrology targets, such as but not limited to metrology metrics. In this regard, the optical imaging subsystem 102 can also be referred to as a metrology tool. The metrology metrics can include but are not limited to the structural and material properties of the sample 104, bandgap, critical dimension (such as the width of a manufacturing feature at a selected height), the overlay of two or more layers, sidewall angle, film thickness, or process-related parameters (such as the focus position of the sample during a lithography step, the exposure dose of the illumination during a lithography step, and the like). The structural properties of the sample 104 can include but are not limited to the dimensional properties of the structures and films associated with various semiconductor manufacturing processes (such as film thickness and / or the critical dimension of the structure, overlay, etc.). The material properties can include but are not limited to the material composition associated with various semiconductor manufacturing processes. The metrology metrics are used to facilitate process control and / or throughput efficiency in semiconductor die manufacturing. It should be recognized here that semiconductor processes (such as depositing a film, lithography steps, etching steps, and the like) performed by semiconductor process tools can drift over time. The drift can be caused by several factors including but not limited to tool wear or the drift of control algorithms associated with the process. In addition, the drift can affect one or more properties of the sample, which in turn can affect one or more metrology measurements (such as metrology metrics proportional to the bandgap, critical dimension measurements, and the like). In this regard, the metrology measurements can provide diagnostic information related to one or more steps in the manufacturing process. The metrology data can be used in the semiconductor manufacturing process for (e.g.) feedforward, feedback, and / or sidefeed correction of processes (such as lithography steps, etching steps, and the like) to provide a complete process control solution.

[0085] In some embodiments, inspection system 100 includes controller 124. Optical imaging subsystem 102 is communicatively coupled to controller 124. In this regard, controller 124 may be configured to receive data including but not limited to metrology data (such as spectral signals, images of targets, pupil images, and the like) or metrology metrics (such as metrology metrics proportional to the bandgap of a multilayer grating, critical dimension, film thickness, composition, overlay accuracy, tool-induced shift, sensitivity, diffraction efficiency, defocus slope, sidewall angle, and the like). In some embodiments, the metrology data includes an indication of the measured spectral response (such as the measured intensity varying according to wavelength) of the sample based on one or more sampling processes from a spectrometer (such as optical imaging subsystem 102).

[0086] Controller 124 may use data from optical imaging subsystem 102 in semiconductor manufacturing processes for, e.g., feedforward, feedback, and / or sidefeed correction processes (such as lithography, etching) and may thus generate a complete process control solution.

[0087] Controller 124 may include one or more processors 126 configured to execute program instructions maintained in a memory 128 (such as a memory medium). In this regard, one or more processors 126 of controller 124 may execute any of the various process steps described in this disclosure. Controller 124 may be communicatively coupled to one or more optical inspection subsystems 102. Controller 124 may receive images from optical inspection subsystem 102. For example, controller 124 may receive images from detector 116.

[0088] One or more processors 126 of controller 124 may include any processing element known in the art. In this sense, one or more processors 126 may include any microprocessor-type device configured to execute algorithms and / or instructions. In one embodiment, one or more processors 126 may consist of a desktop computer, a mainframe computer system, a workstation, an image computer, a parallel processor, or any other computer system (such as a network computer) configured to execute a program configured to operate inspection system 100, as described in this disclosure. It should be further appreciated that the term "processor" may be broadly defined to encompass any device having one or more processing elements that execute program instructions from a non-transitory memory 128.

[0089] Memory 128 may include any storage medium known in the art suitable for storing program instructions executable by one or more associated processors 126. For example, memory 128 may include a non-transitory memory medium. As another example, memory 128 may include, but is not limited to, read-only memory, random access memory, magnetic or optical memory devices (such as magnetic disks), magnetic tapes, solid-state drives, and the like. It should be further noted that memory 128 may be housed together with one or more processors 126 in a common controller housing. In one embodiment, memory 128 may be remotely located relative to the physical location of one or more processors 126 and controller 124. For example, one or more processors 126 of controller 124 may access a remote memory (such as a server) that can be accessed via a network (such as the Internet, an internal network, and the like). Thus, the above description should not be construed as limiting the present invention but is for illustrative purposes only.

[0090] Figure 1B is a simplified schematic diagram of an optical imaging subsystem 102 in accordance with one or more embodiments of the present disclosure.

[0091] Illumination source 110 may include any type of illumination source known in the art suitable for generating optical illumination 108, which may be in the form of one or more illumination beams. Additionally, illumination 108 may have any spectrum, such as, but not limited to, extreme ultraviolet (EUV) wavelengths, ultraviolet (UV) wavelengths, visible light wavelengths, or infrared (IR) wavelengths. Further, illumination source 110 may be a broadband source, a narrowband source, and / or a tunable source.

[0092] In some embodiments, illumination source 110 includes a broadband plasma (BBP) illumination source. In this regard, illumination 108 may include radiation emitted by the plasma. For example, BBP illumination source 110 may include, but does not necessarily include, one or more pump sources (such as one or more lasers) that are configured to focus into a volume of gas to cause energy absorption by the gas to generate or sustain a plasma suitable for emitting radiation. Additionally, at least a portion of the plasma radiation may be used as illumination 108. In another embodiment, illumination source 110 may include one or more lasers. For example, illumination source 110 may include any laser system known in the art capable of emitting radiation in the infrared, visible, or ultraviolet portions of the electromagnetic spectrum.

[0093] Illumination source 110 may generate illumination 108. Illumination 108 may have any temporal profile. For example, illumination 108 may include continuous wave (CW) illumination, pulsed illumination, or modulated illumination. Additionally, illumination 108 may be transmitted from illumination source 110 via free space or guided light (such as an optical fiber, an optical tube, or the like).

[0094] The illumination subsystem 106 and / or the optical imaging subsystem 102 may include various components for directing the illumination 108 to the sample 104, such as but not limited to lenses 118, mirrors, or the like. Additionally, such components may be reflective or transmissive elements. In this manner, Figure 1B the lens 118 in Figure 1B is depicted as a transmissive element for illustration purposes only and not by way of limitation. The illumination subsystem 106 may further include one or more optical elements 120 for modifying and / or adjusting the light in the associated optical path, such as but not limited to one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers. In an embodiment, the illumination subsystem 106 and / or the optical imaging subsystem 102 includes a beam splitter 130 that is oriented to simultaneously direct the illumination 108 to the sample 104 and collect the sample light 114 emitted from the sample 104. In this regard, the illumination 108 and the sample light 114 may share the same path between the beam splitter 130 and the sample 104.

[0095] In some embodiments, the inspection system 100 includes a translation stage 122 for fixing and / or positioning the sample 104 during imaging. For example, the translation stage 122 may include any combination of linear actuators, rotary actuators, angular actuators, flip / tilt stages, and the like. The translation stage 122 may position the sample 104 using any number of degrees of freedom. In this regard, the translation stage 122 may position the sample 104 within the measurement field of view of the illumination 108.

[0096] The optical imaging subsystem 102 may include various components that collect at least a portion of the sample light 114 radiation (e.g., sample light in the case of the optical imaging subsystem 102) emitted from the sample 104 and direct at least a portion of the sample light 114 to the detector 116 for generating an image.

[0097] The inspection system 100 may further image the sample 104 using any technique known in the art. In some embodiments, the inspection system 100 generates an image of the sample 104 in a scanning mode by focusing the illumination 108 as a point or a line onto the sample 104, capturing the point or line image, and scanning the sample 104 to accumulate a two-dimensional image. In this configuration, the scanning may be achieved by moving the sample 104 relative to the illumination 108 (e.g., using the translation stage 122), by moving the illumination 108 relative to the sample 104 (e.g., using an actuatable mirror or the like), or a combination thereof. The scanning may include scanning the sample 104 along a scanning path to produce a trace of the scanning path. In some embodiments, the inspection system 100 generates an image of the sample 104 in a static mode by directing the illumination 108 to the sample 104 within a two-dimensional field of view and directly capturing the two-dimensional image with the detector 116.

[0098] The images generated by inspection system 100 can be of any type known in the art, such as but not limited to brightfield images, darkfield images, phase contrast images, or the like. In some embodiments, the images can be raw images from the optical imaging subsystem 102. In this configuration, the inspection images can include various patterned features on the sample. Additionally, the images can be stitched together to form a composite image of the sample 104 or a portion thereof, but this is not intended to be a limitation of the present disclosure. Although the images have been described as including patterned features, this is not intended to be a limitation of the present disclosure. Further contemplated, the images can be from a sample or wafer without patterned features.

[0099] Detector 116 can include any type of sensor known in the art suitable for measuring sample light 114. For example, detector 116 can include a multi-pixel sensor, such as but not limited to a charge-coupled device (CCD), a complementary metal-oxide semiconductor (CMOS) device, a line sensor, or a time delay integration (TDI) sensor. As another example, detector 116 can include two or more single-pixel sensors, such as but not limited to a photodiode, an avalanche photodiode, a photomultiplier tube, or a single-photon detector. In some embodiments, detector 116 can include a TDI sensor. The TDI sensor can include multiple pixel rows and a readout row. The TDI sensor can include a timing signal that causes charge to move continuously from one pixel row to the next pixel row until the charge reaches the readout row of the row in which the image is generated. By synchronizing the charge transfer (e.g., based on the timing signal) with the movement of the sample in the scan direction, the charge can continuously accumulate across the pixel rows to provide a relatively higher signal-to-noise ratio compared to a line sensor.

[0100] The optical inspection mode can correspond to any combination of parameters for generating an image of the sample 104, including but not limited to the nature of the illumination directed to the sample 104 or the light collected from the sample 104. Additionally, imaging with different optical inspection modes can generally be performed with any number of optical imaging subsystems 102. In some embodiments, one or more optical imaging subsystems 102 can be configured to image the sample 104 with multiple optical inspection modes.

[0101] The optical inspection mode provided by the optical imaging subsystem 102 can be controlled based on any combination of components that control the illumination subsystem 106 or the light collector subsystem 112. For example, the control of the illumination 108 directed to the sample 104 can be provided directly by the illumination source 110 and / or through the optical element 120, such as but not limited to a spectral filter for controlling the wavelength of the illumination 108, a polarizer for controlling the polarization of the illumination 108, or an apodizer for controlling the angular distribution of the illumination 108 on the sample 104 (e.g., in the illumination pupil plane). As another example, the control of the sample light 114 collected from the sample 104 and transmitted to the detector 116 can be provided by the optical element 120, such as but not limited to a spectral filter for controlling the wavelength of the sample light 114 transmitted to the detector 116, a polarizer for controlling the polarization of the sample light 114 transmitted to the detector 116, or an apodizer for controlling the angular distribution of the sample light 114 transmitted to the detector 116 (e.g., in the light collector pupil plane).

[0102] By way of illustration, a particular optical inspection mode can correspond to illumination 108 having a selected spectrum (e.g., as described by bandwidth and / or center wavelength) and a selected polarization (e.g., as defined by an illumination aperture or apodizer) directed to the sample at a selected angle of incidence. The optical inspection mode can further correspond to a particular spectrum and polarization of the sample light 114 directed to the detector 116 (both of which can be the same as or different from the spectrum and polarization of the illumination 108 incident on the sample 104).

[0103] In addition, any of the illumination source 110 and / or the optical element 120 can be adjusted such that the inspection system 100 can be configured to provide different optical inspection modes. For example, any of the optical elements 120 can be directly tuned and / or controlled by an actuator to provide different optical inspection modes. In some embodiments, the controller 124 generates drive signals for any of the illumination source 110 and / or the optical element 120 to selectively provide different optical inspection modes.

[0104] In an embodiment, the optical imaging subsystem 102 can generate one or more images. The images can include inspection images and reference images, as will be further described herein. In an embodiment, the optical imaging subsystem 102 can use one or more optical modes to generate one or more images.

[0105] In view thereof, defects on a sample may respond differently to imaging in different optical modes, such that defect analysis or identification may be improved by considering images generated with different optical modes. Additional embodiments of the present disclosure are directed to inspection systems suitable for performing multi-mode optical inspection. In view thereof, multi-mode inspection may provide performance that is generally superior to single-mode inspection techniques (e.g., differentiating defects from background signals). Additionally, increasing the number of inspection modes generally improves inspection performance. However, it should be further recognized herein that it may be desirable to balance the number of optical inspection modes used during inspection, particularly when such multi-mode inspection requires multiple imaging scans and thus takes longer to perform.

[0106] In some embodiments, a single optical imaging subsystem 102 may be configured to image a sample 104 simultaneously or sequentially with multiple optical inspection modes. In some embodiments, different optical imaging subsystems 102 are used to provide at least some of the different optical inspection modes.

[0107] In some embodiments, the inspection system 100 provides images sequentially with different optical inspection modes. For example, the inspection system 100 may sequentially switch between different optical imaging subsystems 102 and / or adjust the parameters of the optical imaging subsystem 102 to provide sequential images of the sample 104 with different optical inspection modes.

[0108] In some embodiments, the optical imaging subsystem 102 may be configured to simultaneously provide two or more images with different optical inspection modes. By way of illustration, the optical imaging subsystem 102 may include two or more light collection channels each having a separate detector 116. The optical imaging subsystem 102 may then have one or more beam splitters for splitting the sample light 114 into the various channels and / or additional optical elements 120 (e.g., individual spectral filters, polarizers, or the like) for providing separate control of the nature of the sample light 114 directed to the associated detector 116 in each channel.

[0109] Figure 1C is a simplified schematic diagram of an optical imaging subsystem 102 in accordance with one or more embodiments of the present disclosure.

[0110] In one embodiment, the optical imaging subsystem 102 includes an illumination source 110 for generating illumination 108. The illumination 108 may include light of one or more selected wavelengths, including but not limited to ultraviolet (UV) radiation, visible light radiation, or infrared (IR) radiation. For example, the illumination source 110 may include but not limited to one or more narrowband laser sources, one or more broadband laser sources, one or more supercontinuum laser sources, one or more white light laser sources, and the like. In this regard, the illumination source 110 may provide illumination 108 with high coherence (e.g., high spatial coherence and / or temporal coherence). In another embodiment, the illumination source 110 includes a laser-driven light source (LDLS), such as but not limited to a laser sustained plasma (LSP) source. For example, the illumination source 110 may include but not limited to an LSP lamp, an LSP bulb, or an LSP chamber suitable for accommodating one or more elements that can emit broadband illumination when excited into a plasma state by a laser source. In another embodiment, the illumination source 110 includes a lamp source. As another example, the illumination source 110 may include but not limited to arc lamps, discharge lamps, electrodeless lamps, and the like. In this regard, the illumination source 110 may provide illumination 108 with low coherence (e.g., low spatial coherence and / or temporal coherence).

[0111] In another embodiment, the illumination source 110 is configured to provide illumination at wavelengths around the expected bandgap of a test layer having a multilayer grating structure (such as but not limited to a "high-k" insulating layer having a bandgap in the UV spectral region or a layer of a memory structure having a bandgap in the IR spectral region). For example, the illumination source 110 may include but not necessarily include an LDLS that provides wavelengths in a spectral range between about 120 nanometers and about 3 micrometers. As another example, the illumination source 110 may provide wavelengths greater than about 150 nanometers suitable for determining the bandgap of an insulating layer. As a further example, as another example, the illumination source 110 may provide wavelengths greater than about 700 nanometers suitable for determining the bandgap of a layer of a memory structure.

[0112] In another embodiment, the illumination source 110 provides tunable illumination 108. For example, the illumination source 110 may include a tunable illumination source (such as one or more tunable lasers and the like). As another example, the illumination source 110 may include a broadband illumination source coupled to a tunable filter.

[0113] The illumination source 110 may further provide illumination 108 having any temporal profile. For example, the illumination 108 may have a continuous temporal profile, a modulated temporal profile, a pulsed temporal profile, and the like.

[0114] In another embodiment, the illumination source 110 directs illumination 108 to the sample 104 via the illumination path of the illumination subsystem 106 and collects the radiation emitted from the sample via the light collection path of the light collection subsystem 112. The illumination path may include one or more beam conditioning components suitable for modifying and / or adjusting the illumination 108. For example, the one or more beam conditioning components may include, but are not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers or one or more lenses.

[0115] In another embodiment, the illumination subsystem 106 may utilize one or more lenses 118 to focus the illumination 108 onto the sample 104. The illumination subsystem 106 may further include one or more optical elements 120 for modifying and / or adjusting the light in the associated optical path, such as, but not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers.

[0116] In another embodiment, the light collection subsystem 112 may include one or more lenses 118 for collecting radiation from the sample 104. The light collection subsystem 112 may further include one or more optical elements 120 for modifying and / or adjusting the light in the associated optical path, such as, but not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers.

[0117] In another embodiment, the optical imaging subsystem 102 includes a detector 116 configured to capture the radiation emitted from the sample 104 via the light collection path. For example, the detector 116 may receive radiation reflected or scattered from the sample 104 (e.g., via specular reflection, diffuse reflection, and the like). As another example, the detector 116 may receive radiation generated by the sample 104 (e.g., luminescence associated with absorption of the illumination 108 and the like). As another example, the detector 116 may receive one or more diffraction orders of the radiation from the sample 104 (e.g., 0th order diffraction, ±1st order diffraction, ±2nd order diffraction, and the like).

[0118] The detector 116 may include any type of optical detector known in the art suitable for measuring the illumination received from the sample 104. For example, the detector 116 may include, but is not limited to, a CCD detector, a CMOS detector, a TDI detector, a photomultiplier tube (PMT), an avalanche photodiode (APD), and the like. In another embodiment, the detector 116 may include a spectral detector suitable for identifying the wavelength of the radiation emitted from the sample 104.

[0119] The photon collection subsystem 112 may further include any number of collection beam conditioning elements for guiding and / or modifying the collected illumination, including but not limited to one or more lenses, one or more filters, one or more polarizers, or one or more phase plates. In this regard, the optical imaging subsystem 102 may be configured as any type of metrology tool, such as but not limited to a spectroscopic ellipsometer having one or more illumination angles, a spectroscopic ellipsometer for measuring Mueller matrix elements (e.g., using a rotating compensator), a single-wavelength ellipsometer, an angular-resolved ellipsometer (e.g., a beam-profile ellipsometer), a spectroscopic reflectometer, a single-wavelength reflectometer, an angular-resolved reflectometer (e.g., a beam-profile reflectometer), an imaging system, a pupil imaging system, a spectral imaging system, or a scatterometer.

[0120] In addition, it should be noted here that the depicted optical imaging subsystem 102 may facilitate multi-angle illumination of the sample 104 and / or more than one illumination source 110 coupled to one or more additional detectors. In this regard, the optical imaging subsystem 102 may perform multiple metrology measurements.

[0121] In another embodiment, one or more optical components may be mounted to a rotatable arm (not shown) that pivots around the sample 104 such that the angle of incidence of the illumination 108 on the sample 104 can be controlled by the position of the rotatable arm. In another embodiment, the optical imaging subsystem 102 may include multiple detectors (e.g., associated with multiple beam paths created by one or more beam splitters) to facilitate multiple metrology measurements (e.g., multiple metrology tools) through the optical imaging subsystem 102.

[0122] Figure 2A is a perspective view of the structure 200 of the sample 104 according to one or more embodiments of the present disclosure. The structure 200 generally refers to one or more structures, samples, metrology targets, or the like of the sample 104. In some embodiments, the structure to be measured includes two or more geometric features each made of a different material. The geometric features may define various semiconductor transistors. For example, the structure 200 may include but not be limited to a thin film stack, a fin field-effect transistor (FinFET), a gate-all-around (GAA) transistor (e.g., a GAA FET), a partially fabricated transistor structure, and future generations of DRAM and 3D flash memory structures. As depicted, the structure 200 is a post-nanosheet release GAA model (unit cell).

[0123] In an embodiment, the structure 200 may include one or more nanosheets 202. The nanosheets 202 may be two-dimensional nanostructures having a thickness in the range of 1 nm to 100 nm. For example, the nanosheets 202 may include a nanosheet profile having a thickness of 5 nanometers or less. In the depicted example, the structure 200 is a GAA FET and the nanosheets 202 are silicon nanosheets serving as conductive channels in the GAA transistor, but this is not intended to be limiting. The nanosheets 202 are surrounded by a series of materials forming the gate of the device. The encapsulating materials include materials such as silicon dioxide, hafnium oxide, titanium nitride, tantalum nitride, and the like. The encapsulating materials are deposited on the nanowires using an atomic layer deposition process to form a gate surrounding the nanowire channels.

[0124] When the thickness of the nanosheets 202 in a transistor reaches below 5 nanometers (less than 5 nm), nanoscale local thickness fluctuations become critical to the performance of the sample 104. When the thickness of the nanosheets is non-uniform, several unwanted effects may occur, including but not limited to performance variability from one transistor to another, performance variations from one nanosheet to another within the same transistor, threshold voltage drift of the drive current from the design expectation, and / or change in the cut-off state leakage.

[0125] In some embodiments, the local thickness fluctuations of the nanosheets 202 are induced by the surface roughness of the nanosheets 202. In some embodiments, the carrier mobility is sensitive to the thickness. When the vertical dimension of the roughness is large enough compared to the average thickness of the horizontal nanosheet, the carrier mobility may vary significantly as it passes through the channel. The carrier velocity and other dynamic parameters also change from one point to another in the cross-section of the nanosheet due to the surface non-uniformity.

[0126] Although most of the present disclosure is described in the context of nanosheets, this is not intended to be a limitation of the present disclosure. Further considered, embodiments of the nanosheets may equally apply to transistors and nanowires. In this regard, nanosheets and nanowires may be used interchangeably herein.

[0127] Now referring specifically to Figure 2B , a nanosheet 202 including roughness having an average thickness (t), a roughness amplitude (δ), and a correlation length (wavelength) Γ is illustrated. The surface roughness can be quantified based on the root mean square of the roughness amplitude δ and the correlation length (wavelength) Γ. In this example, the nanosheet 202 is in a post-nanosheet release process, but this is not intended to be limiting. As depicted, the surface roughness of the nanosheet 202 is anisotropic.

[0128] For a GAA transistor, the nanosheets are relatively narrow to experience large variations in the sub-band energy. The energy of the confined carriers varies according to the nanosheet thickness t and the associated discrete energy is given as follows:

[0129]

[0130] where E is the energy in the nanosheet, is Planck's constant, n is an integer quantum number, m is the carrier effective mass, and k is the wave vector associated with each energy level (k = nπ / t). The energy in the quantum nanosheet is inversely proportional to the square of the nanosheet thickness t.

[0131] The effective mass and mobility μ are linked as follows:

[0132] μ = qτ / m

[0133] where q is the carrier charge and τ is the carrier lifetime.

[0134] A perturbation in the nanosheet thickness from t to t + δ is directly translated into a fluctuation in the energy level En across the nanosheet, which itself manifests as a variation in the effective mass and the carrier mobility μ. This n random fluctuation in E will scatter the electron and hole carriers and will result in the mobility varying with the nanosheet thickness as given below:

[0135]

[0136] The equation for the carrier mobility μ is valid for materials with low effective mass (e.g., Si (0.187m0 for electrons)). The equation for the carrier mobility μ establishes a direct and quantitative relationship between the random variation in the nanosheet thickness due to interface or surface roughness and the carrier mobility. Any strong variation in the roughness will result in device performance degradation.

[0137] The main factor contributing to abnormal surface roughness occurs during the process after nanosheet release. The optimization of the GAA process from the superlattice film stack to nanosheet release (specifically, wet etching) should be carried out in such a way that the nanosheet surface remains as flat as possible. Therefore, a non-destructive, high-throughput, and accurate metrology method is needed that can monitor the nanosheet roughness and then mitigate the nanosheet roughness to ensure that the final device performance meets the design specifications.

[0138] The profile of the nanosheet 202 may include at least one of a rhombic cross-section, an elliptical cross-section, a triangular cross-section, a rectangular cross-section, or a trapezoidal cross-section. The profile of the nanosheet 202 may include a thickness of 5 nanometers or less.

[0139] Reference is now made to Figure 3 , and the model construction and analysis engine 300 is described in accordance with one or more embodiments of the present disclosure. The controller 124 is configured to execute the model construction and analysis engine 300. The model construction and analysis engine 300 is a set of program instructions stored in the memory 128. The program instructions are executed by one or more processors 126 to implement the model construction and analysis functions.

[0140] The model construction and analysis engine 300 is configured to receive one or more inputs, such as but not limited to user input 302 and / or measurement data 304. In some embodiments, the controller 124 is configured to receive the user input 302 from a user input source 306 (such as a graphical user interface, a keyboard, and the like) of the inspection system 100. In some embodiments, the controller 124 is configured to receive the measurement data 304 from the detector 116. The measurement data 304 may include but not be limited to the measurement spectra of the structure 200 of the sample 104 detected by the detector 116. The measurement data 304 may include various values of a set of given measurement system parameter values (such as the incident angle, azimuth angle, illumination polarization, electric field orientation, etc.).

[0141] In some embodiments, the model construction and analysis engine 300 includes a structure model construction module 308. The structure model construction module 308 generates a structure model 310. The structure model construction module 308 may generate the structure model 310 at least in part based on the user input 302. In some embodiments, the structure model construction module 308 is implemented in an AcuShape software product manufactured by KLA Corporation, Milpitas, Calif. (USA). In one example, the AcuShape software includes a set of geometric features (such as 1D layers, 2D trapezoids, 3D columns, etc.) joined together and parameterized to simulate the structure to be measured. Additionally, the AcuShape software includes a set of building blocks that can be used by the user to assign material behavior to any modeled structural feature. In this way, the user input 302 may include the selection of which material (i.e., which part of the modeled structure) will be characterized by the dispersion properties.

[0142] In some embodiments, the structure model 310 results in the structure of the sample 104 (such as the structure 200). For example, the structure model 310 may be a semiconductor structure based on nanosheets and / or nanowires. In some embodiments, the structure model 310 further includes the material properties of the target. In some embodiments, the structure model 310 includes the characterization of the optical dispersion properties of one or more of these different materials. Generally speaking, the structure model 310 may include any optical dispersion model. By way of non-limiting examples, the dispersion models include the Bruggeman effective medium approximation (EMA) (BEMA) model, the Cody-Lorentz model, the Tauc-Lorentz model, the harmonic oscillator model, and the point-to-point dispersion model.

[0143] The components for semiconductor metrology in a device or device-like target use an electromagnetic solver to model the optical interaction of an incident beam with a sample. In some embodiments, the modeling and analysis engine 300 includes an optical response function construction module 312. The structural model 310 receives as an input to the optical response function construction module 312. The optical response function construction module 312 generates an optical response function model 314 based at least in part on the structural model 310. In some embodiments, the optical response function construction module 312 uses an electromagnetic solver to characterize the optical interaction of an incident beam with a structure to be measured using algorithms such as: rigorous coupled wave analysis (RCWA), finite element method (FEM), method of moments, surface integral method, volume integral method, finite difference time domain (FDTD) method, and other simulation algorithms. Any of the simulation algorithms may rely on a predetermined dispersion of the individual components of the measurement target. Given the geometric model 310 along with the dispersion parameters (e.g., n and k) of the different parts of the structure, the optical response function construction module 312 may solve some form of Maxwell's equations and / or the Schrödinger equation. This solution can then be used to derive a simulated signal. The RCWA method can determine a structure from a measurement spectrum by solving Maxwell's equations and the structural dielectric function expanded as a Fourier series. The RCWA method requires the measurement of a periodic structure. Thus, the RCWA assumes an interaction of the electric field with a repeating grating. In some embodiments, the optical dispersion model described herein is implemented in the film thickness measurement library (FTML) of the offline spectral analysis (OLSA) stand-alone software available from KLA-Tencor Corporation of Milpitas, California, USA.

[0144] The optical response function model 314 can be the modeled optical response of the sample 104 and / or the target (e.g., the structure 200). The modeled optical response can include various values determined for a given set of measurement system parameter values (e.g., angle of incidence, azimuthal angle, illumination polarization, electric field orientation, etc.).

[0145] In some embodiments, the modeling and analysis engine 300 includes a fitting analysis module 316. The optical response function model 314 and / or the measurement data 304 are received as inputs to the fitting analysis module 316. In some instances, the fitting analysis module 316 resolves at least one sample parameter value by performing a fitting analysis of the measurement data 304 with the optical response function model 314.

[0146] The fitting analysis module 316 analyzes the measurement data 304 through any number of different data fitting and optimization techniques. By way of non-limiting example, the fitting analysis module 316 may implement library matching techniques, fast reduced-order modeling techniques, regression, machine learning algorithms (such as neural networks), support vector machines (SVMs), dimensionality reduction algorithms (such as principal component analysis (PCA), independent component analysis (ICA)), local linear embedding (LLE), sparse representation techniques (such as Fourier or wavelet transform techniques), Kalman filtering, and algorithms for facilitating matching across the same or different tool types, among others. Fitting of spectral measurement data is beneficial for any type of optical technique that provides sensitivity to geometric and / or material parameters of interest. The sample parameters may be deterministic (such as CD, SWA, etc.) or statistical (such as the rms height of sidewall roughness, roughness correlation length, etc.), as long as an appropriate model describing the interaction of the light beam with the sample is used.

[0147] Regression can be used to minimize an error function (such as the square of the difference between the simulated and measured signals) in the space of unknown parameters (such as geometric parameters, material parameters, other parameters). In an example, the unknown parameters are repeatedly guessed until the simulated spectrum in the optical response function model 314 closely matches the measured spectrum in the measurement data 304. In an example of machine learning, the model can be trained based on a simulator that can output the unknown parameters from a given spectrum. Once the model is available, feeding the measured spectrum into the model can output the resulting values of the unknown parameters.

[0148] The fitting analysis module 316 compares the optical response function model 314 with the corresponding measurement data 304 to generate a parameter sub-structure model 318. The parameter sub-structure model 318 can be a structural model of a target (such as a nanosheet- or nanowire-based semiconductor structure to be measured). The parameter sub-structure model 318 can be considered reusable. The parameter sub-structure model 318 may include values of the optical properties, geometric properties, and / or material properties of the sample 104.

[0149] In some embodiments, the parameter sub-structure model 318 is a machine learning-based model (such as a neural network model, linear model, polynomial model, response surface model, support vector machine model, random forest model, or other types of models). The machine learning-based model is trained based on spectral signals collected from metrology targets with known geometric profiles (such as geometric profiles accurately measured by a reference metrology system (such as the X-ray and electron-based metrology systems described above)). In some embodiments, the parameter sub-structure model 318 is determined based on measurement training data (such as spectra collected from a design of experiments (DOE) wafer). The parameter sub-structure model 318 can then be used to directly calculate process parameter values, structural parameter values, or both from measurement data (such as spectra) collected from other wafers.

[0150] Accordingly, the controller 124 is configured to generate a structural model 310 (e.g., a geometric model, a material model, or a combined geometric and material model) of the measurement structure of the sample 104, generate an optical response model 314 including at least one geometric parameter from the structural model 310, and resolve at least one parameter value by performing a fitting analysis of the optical measurement data 304 and the optical response model 314.

[0151] In some embodiments, the inspection system 100 is configured to store the parameter sub-structure model 318 in the memory 128. The parameter sub-structure model 318 may then be one of a pre-computed model library for determining values of at least one parameter value associated with the sample 104.

[0152] In some embodiments, the controller 124 is configured to access model parameters in real time using real-time critical dimensioning (RTCD), or it may access a pre-computed model library for determining values of at least one parameter value associated with the sample 104. Some forms of the CD engine may be used to evaluate the difference between the assigned CD parameters and the CD parameters associated with the measurement data 304 of the sample 104. The controller 124 uses the model construction and analysis engine 300 to compare the simulated optical response signal with the measurement data 304, thereby allowing determination of the geometric and material properties of the sample 104.

[0153] Reference is now made to Figure 4A , an effective medium approximation (EMA) model profile 400 is described in accordance with one or more embodiments of the present disclosure. The EMA model profile 400 is an example of the structural model 310 provided to the optical response function construction module 312. The EMA model profile 400 is an isotropic EMA. The isotropic EMA uses two layers to approximately calculate the surface roughness of the profile of the nanosheet 202. The EMA model profile 400 includes a homogeneous layer 402 and a rough layer 404. The nanosheet 202 is represented by the homogeneous layer 402 and the rough layer 404. In this regard, the nanosheet 202 is represented as two parts.

[0154] The homogeneous layer 402 includes a thickness derived by subtracting the surface roughness from the thickness of the nanosheet 202. The homogeneous layer 402 is assigned a dispersion parameter (e.g., a regular Si dielectric function).

[0155] The rough layer 404 can also be referred to as a surface layer or an interface layer. The rough layer 404 is inhomogeneous and contains a mixture of materials due to surface roughness. The rough layer 404 is isotropic. The rough layer 404 is a cladding material surrounding the homogeneous layer 402. The rough layer 404 contains a thickness combined with a roughness amplitude. The rough layer 404 contains dispersion parameters simulated using the effective medium approximation (EMA). The dispersion relation then approximately calculates the dispersion of the surface roughness. EMA is feasible when the local variation of the permittivity associated with the surface roughness is less than the wavelength of the light interacting with the medium. The rough layer 404 contains an EMA determined to vary based on the material of the nanosheet 202 and a second material. For example, the material of the nanosheet 202 can be silicon and the second material can be air, but this is not intended to be limiting. The dispersion parameters are simulated as a mixture of silicon and air. The mixture of silicon and air can be constant and / or floating.

[0156] In some embodiments, the mixture of silicon and air is constant. For example, the EMA dielectric function can be simulated as a mixture of 50% Si and 50% air. The mixture of 50% Si and 50% air can pose a risk of roughness accuracy measurement because the actual medium is not in a 50:50 ratio. These inaccuracies are not negligible for a nanosheet thickness of about 5 nm.

[0157] In some embodiments, the fraction of EMA floats in the model and is constrained by the roughness thickness standard deviation σ. The conversion factor between the EMA fraction and σ is experimentally determined through design of experiments. σ is the standard deviation of the nanosheet thickness measured at several positions along the gate. A model based on RCWA is then created to relate the EMA to the roughness index σ. Extracting the roughness amounts to solving the Maxwell equations with the modeled dielectric function of the structure containing the EMA. The assumption verified by the actual process is that the roughness index is periodic within the measurement points.

[0158] Therefore, the EMA model profile 400 can be used as the geometric model 310 and approximately calculates the surface roughness of the nanosheet 202 profile. The optical response function model 314 of the structure 200 of the sample 104 with respect to the illumination 108 is generated at least in part based on the geometric model 310 (e.g., the EMA model profile 400). The optical response function model 314 then simulates the optical response of the nanosheet 202 profile with surface roughness to the illumination 108. For example, the optical response function model 314 uses the dispersion parameters of the homogeneous layer 402 and the rough layer 404 to simulate the optical response. Since the roughness parameter has low sensitivity, the optical response function model 314 is provided to generate a parametric substructure model 318 (e.g., a machine learning model) at least based on the optical response function model 314. The low amount of roughness compared to the entire structure makes it difficult to detect its variation from other highly sensitive parameters. In this regard, the RCWA conventional model is used to simulate the basic process variations.

[0159] An experiment using the EMA model profile 400 is now described. An EMA model profile 400 with a varying nanosheet thickness 3 sigma (3σ) between 0.3 nm and 2.6 nm is used to generate a set of 400 synthetic spectra. The set of synthetic spectra is used to train a parametric substructure model 318 (e.g., a neural network model). The parametric substructure model 318 is then validated with a blind test set of 50 spectra. The parametric substructure model 318 is determined to extract the nanosheet roughness 3σ to an acceptable accuracy of 0.97 R-squared from the blind test set. For example, using the full Mueller matrix spectra, the EMA model profile 400 experiment is determined to an accuracy of R-squared values between 0.9718 and 0.9777.

[0160] Now referring Figures 4B to 4C ..., plots 406a to 406b of the dispersion parameters of the EMA model profile 400 are depicted in accordance with one or more embodiments of the present disclosure. The dispersion parameters may also be referred to as optical properties within one or more illumination wavelengths. Plots 406a to 406b include the dispersion parameters of the homogeneous layer 402 and the dispersion parameters of the rough layer 404. Plots 406a to 406b are plotted over the illumination wavelength range. For example, plots 406a to 406b are plotted in the range from 150 nm to 950 nm, but this is not intended to be limiting.

[0161] Plot 406a depicts the real part of the dispersion parameter, also referred to as the refractive index (n). Plot 406a includes plot line 408a and plot line 410a. Plot line 408a depicts the refractive index (n) of the rough layer 404 within the illumination wavelength. Plot line 410a depicts the refractive index (n) of the homogeneous layer 402 within the illumination wavelength.

[0162] Plot 406b depicts the imaginary part of the dispersion parameter, also referred to as the extinction coefficient (k). Plot 406b includes plot line 408b and plot line 410b. Plot line 408b depicts the extinction coefficient (k) of the rough layer 404 within the illumination wavelength. Plot line 410b depicts the extinction coefficient (k) of the homogeneous layer 402 within the illumination wavelength.

[0163] In this example, plot lines 408a and 408b are for the rough layer 404 with a mixture of 50% air and 50% silicon. Plot lines 408a and 408b can be determined using the effective medium approximation (EMA) of the rough layer 404. Plot lines 410b and 410b are for the homogeneous layer of silicon (Si). Plot lines 410b and 410b may also be referred to as the regular Si dielectric function or dispersion relation of the homogeneous layer 402.

[0164] Now referring Figures 5A to 5B, Building block 500 is described in accordance with one or more embodiments of the present disclosure. Building block 500 is an example of the structural model 310 provided to the optical response function construction module 312. Building block 500 is anisotropic and includes a height that varies along a direction. Building block 500 approximately calculates the surface roughness of the profile of the nanosheet 202 by varying the height.

[0165] Building block 500 may also be referred to as a surface shape building block, a flexure shape building block, a nanosheet building block, and the like. Building block 500 supports detailed surface profile control. Building block 500 can accelerate the result time and provide accurate data. Building block 500 is an RCWA-based method for measuring the height of a nanosheet along a channel. Considering this, building block 500 provides modeling flexibility for applications such as GAA, fork-sheet transistors, complementary field-effect transistors (CFETs), and the like.

[0166] Building block 500 uses one or more parameters to define the nanosheet 202. The building block provides various height shape flexibilities and is fully defined by the parameter values. The parameters can be received as user input 302 to the structural model construction module 308. In some embodiments, building block 500 may include a profile design modeled by segments 502 and / or polynomial functions 506. The parameters can include any function for defining the segments and / or polynomial functions 506.

[0167] Now referring specifically to Figure 5A , building block 500 includes segments 502. The parameters can include the number of segments 502, the height HT(i) of each segment 502, and / or the height ratio HTRatio(i) of each segment 502. The height HT(i) and / or the height ratio HTRatio(i) can be floated to design a building block profile that approximately represents the profile of the nanosheet 202. The number of segments 502, the height HT(i) of each segment 502, and / or the height ratio HTRatio(i) of each segment 502 can be received as user input 302. The height HT(i) can also be referred to as the segment height. The height ratio HTRatio(i) can also be referred to as the critical dimension along the direction. The segment height is defined at the critical dimension along the direction.

[0168] Segments 502 can include shapes. Considering this, segments 502 can include rhombic primitive nanowire building blocks, elliptical primitive nanowire building blocks, triangular primitive nanowire building blocks, square primitive nanowire building blocks, trapezoidal primitive nanowire building blocks, cylindrical primitive nanowire building blocks, rectangular or plate-shaped primitive nanowire building blocks, hexagonal primitive nanowire building blocks, stepped primitive nanowire building blocks, slender primitive nanowire building blocks, or any combination thereof. As depicted, segment 502 is a plate and building block 500 includes a stepped shape, but this is not intended to be limiting. The staircase approximation method is applied to each of the segments 502.

[0169] In some embodiments, the building block 500 supports combinations of multiple types of shapes along a direction. In this regard, the segment 502 can include any combination of rhombic primitive nanowire building blocks, elliptical primitive nanowire building blocks, triangular primitive nanowire building blocks, square primitive nanowire building blocks, trapezoidal primitive nanowire building blocks, cylindrical primitive nanowire building blocks, rectangular or plate-shaped primitive nanowire building blocks, hexagonal primitive nanowire building blocks, stepped primitive nanowire building blocks, elongated primitive nanowire building blocks, and the like.

[0170] The junction points between the shapes can be specified according to one or more critical dimensions. The critical dimensions can include the height HT(i) and / or the height ratio HTRatio(i).

[0171] The height ratio HTRatio(i) of each segment 502 can be reported as a fixed width or a percentage width. In some embodiments, the height ratio HTRatio(i) can be defined as the % of the critical dimension of the nanosheet 202 from the edge along the direction, also referred to as the percentage critical dimension from the edge. For example, the height ratio HTRatio(3) can be defined as 50% from the edge along the x direction. In some embodiments, the height ratio HTRatio(i) can be defined as a fixed position from the edge along the direction, also referred to as the fixed critical dimension from the edge. For example, the height ratio HTRatio(3) can be defined as 5 nm from the edge along the x direction.

[0172] The height HT(i) of each segment 502 can be reported as a fixed height or a percentage height. In some embodiments, the height HT(i) can be defined as the % of the height or thickness of the nanosheet 202, also referred to as the percentage segment height. For example, the height ratio HT(3) can be defined as 100% of the nanosheet thickness. In some embodiments, the height ratio HT(i) can be defined as a fixed height, also referred to as the fixed segment height. For example, the height HT(3) can be defined as 5 nm thickness.

[0173] The resolution of the building block 500 can be adjusted by adjusting the number of segments 502. For example, the resolution can be increased by increasing the number of segments 502. If computational resources permit, then the number of segments and similarly the resolution can be increased. Increasing the resolution can enable the building block 500 to better match the morphology of the nanosheet 202. As depicted, the building block has a resolution of 5 segments 502, but this is not intended to be a limitation of the present disclosure. It is contemplated that the building block can have a resolution of 20 segments, 50 segments, or more. The resolution is implemented to control the surface variation / horizontal slicing in the building block.

[0174] Now specifically referring to Figure 5B, the building block 500 is defined by one or more polynomial functions 506. The building block 500 includes a surface 504. The polynomial function 506 defines the surface 504. The height of the surface can be defined as a differential height (dHT) that varies according to a critical dimension (CD) along a direction. As depicted, the polynomial function 506 is defined for a critical dimension (CD x ) along the x direction. Further considered, the polynomial function 506 can be defined for critical dimensions along the x direction and / or the y direction. In this regard, the differential height (dHT) can be defined as a polynomial function that varies according to the CD along x or y. Considered, the polynomial function 506 can include any polynomial function to account for all possible surface shapes of the nanosheet 202. The polynomial function 506 of the surface 504 can be received as a user input 302.

[0175] The building block 500 includes a surface 504a and a surface 504b. The surface 504a is opposite to the surface 504b. The surface 504a is defined by a polynomial function 506a and the surface 504b is defined by a polynomial function 506b. The height of the building block 500 is defined by the polynomial function 506a and the polynomial function 506b. The polynomial function 506a can be the same as and / or different from the polynomial function 506b. The user input 302 can include any polynomial function 506a for the surface 504a, followed by the same or different polynomial function 506b for the surface 504b. The polynomial function 506 then defines the surface shape of the nanosheet along the channel.

[0176] Referring generally again to Figures 5A to 5B , the building block 500 is described. The building block 500 can thus be used as a geometric model 310 and approximately calculate the surface roughness of the profile of the nanosheet 202. The optical response function model 314 of the structure 200 of the sample 104 to the illumination 108 is generated at least in part based on the geometric model 310 (such as the building block 500). The optical response function model 314 then simulates the optical response of the profile of the nanosheet 202 with surface roughness to the illumination 108. For example, the optical response function model 314 performs RCWA on the building block 500 to generate a synthetic spectrum with pre-layer process variations to mimic real-time in-line measurement performance. The advantage of using the building block 500 is that it is no longer necessary to approximately calculate the surface roughness using the effective medium approximation. The optical response function model 314 is provided to generate a parametric substructure model 318 (such as a machine learning model) at least based on the optical response function model 314.

[0177] The parametric substructure model 318 is capable of measuring sheet-specific roughness (such as roughness amplitude and correlation length) and / or the height along the nanosheet.

[0178] In some embodiments, the parameter of interest may be the surface roughness of the nanosheet 202. The surface roughness of the nanosheet 202 may be defined by a roughness amplitude (δ) and a correlation length (Γ). The roughness may be quantified by the standard deviation of the height along the nanosheet. In this regard, the building block 500 provides a method for performing sheet-specific roughness measurements using the building block 500.

[0179] An experiment for determining the roughness of a nanosheet using the building block 500 is now described. A set of 450 synthetic spectra are generated while varying the basic parameters. The parameters are varied to mimic real-time in-line measurements. The set of synthetic spectra is used to train the parameter substructure model 318. The parameter substructure model 318 is then validated with a blind test set of 50 spectra. The standard deviation of the height varies independently between 0.5 nm and 2.6 nm for each nanosheet. The parameter substructure model 318 is determined to extract the nanosheet roughness with an acceptable accuracy of 3σ to 0.97 R-squared from the blind test set. For example, the full Mueller matrix of a combined appropriate model (such as the building block 500) can experimentally track the accuracy of the nanosheet roughness of 3σ to an R-squared value between 0.9700 and 0.9819.

[0180] In some embodiments, the parameter of interest may be one or more heights along the nanosheet 202. The building block 500 enables the parameter substructure model 318 to report the height. The user input 302 may include the height at a position from the edge of the nanosheet 202. The parameter substructure model 318 may receive the measurement data 304 and report the height at a position from the edge of the nanosheet 202 based on the measurement data 304. The height may be regarded as the parameter of interest. For example, the parameter substructure model 318 reports a height of 5 nm from the edge. In this regard, the building block 500 provides a method for performing sheet-specific shape continuous profile measurements using the building block 500.

[0181] An experiment using the building block 500 to determine the height at five positions along the nanosheet 202 is now described. A set of 400 synthetic spectra is generated while varying the basic parameters. The parameters are varied to mimic real-time in-line measurements. The set of synthetic spectra is used to train the parameter substructure model 318. The parameter substructure model 318 is then validated with a blind test set of 50 spectra. In some embodiments, the parameter substructure model 318 is capable of tracking the height of a nanosheet with a thickness of 5 nm and an accuracy of 0.5 nm. The parameter substructure model 318 is determined to extract the height from the blind test set to an acceptable accuracy of 0.90 R-squared. For example, the building block 500 is experimentally determined to include R-squared values for the height at the first position with an R-squared of 0.9083, the height at the second position with an R-squared of 0.9265, the height at the third position with an R-squared of 0.9376, the height at the fourth position with an R-squared of 0.9250, and the height at the fifth position with an R-squared of 0.9073.

[0182] Figure 6 FIG. 4 is a flow chart illustrating the steps performed in method 600 according to one or more embodiments of the present disclosure. The embodiments and implementation techniques previously described herein in the context of the inspection system 100, the EMA model profile 400, and the building block 500 should be interpreted as extending to method 600. However, it should be further noted that method 600 is not limited to the inspection system 100, the EMA model profile 400, and the building block 500.

[0183] In step 610, a geometric model of the structure of the sample is generated. The structure includes a nanosheet profile with surface roughness. The geometric model approximately calculates the surface roughness of the nanosheet profile. In some embodiments, user input may be received from a user input source. The geometric model of the structure may be generated at least in part based on the user input.

[0184] In some embodiments, the geometric model approximately calculates the surface roughness of the nanosheet profile by representing the nanosheet profile as a homogeneous layer and a rough layer. The rough layer is a cladding material surrounding the homogeneous layer. The rough layer is isotropic and the surface roughness is anisotropic. The homogeneous layer includes a material. The homogeneous layer includes one or more dispersion parameters associated with the material. The one or more dispersion parameters include the refractive index (n) and the extinction coefficient (k). Similarly, the rough layer includes one or more dispersion parameters determined using the effective medium approximation. The one or more dispersion parameters include the refractive index (n) and the extinction coefficient (k). The rough layer is a mixture of a first material and a second material in a certain ratio. The first material is different from the second material. The ratio is a fixed ratio and / or a floating ratio.

[0185] In some embodiments, the geometric model approximates the surface roughness of the nanosheet profile using building blocks. The height of the building blocks varies along a direction.

[0186] In some embodiments, the height of the building blocks is defined by a plurality of segments. Each of the plurality of segments includes a segment height at a critical dimension along the direction. The segment height can be defined as either a fixed segment height or a percentage segment height. The critical dimension is defined as either a fixed critical dimension from an edge or a percentage critical dimension. The plurality of segments can be plates and the building block can include a stepped shape. The resolution of the height of the building block is adjusted by adjusting the number of the plurality of segments.

[0187] In some embodiments, the height of the building blocks is defined by one or more polynomial functions. The nanosheet profile includes a first surface and a second surface. The first surface is opposite to the second surface. The first surface is defined by a first polynomial function and the second surface is defined by a second polynomial function. The height of the building blocks is defined by the first polynomial function and the second polynomial function. The first polynomial function may or may not be different from the second polynomial function.

[0188] In step 620, an optical response function model of the structure with respect to illumination is generated based at least in part on the geometric model. The optical response function model simulates the optical response of the nanosheet profile with surface roughness to illumination. In some embodiments, the optical response function model is generated using rigorous coupled wave analysis (RCWA).

[0189] In step 630, measurement data is received from a detector. The measurement data includes the measured spectrum of the structure detected by the detector.

[0190] In step 640, a parametric substructure model is generated based at least on the optical response function model and the measurement data. In some embodiments, the parametric substructure model is a neural network model trained using the optical response function model and the measurement data.

[0191] In step 650, one or more parameters of the structure are extracted based on the measurement data. The one or more parameters can include the standard deviation of the surface roughness, the roughness amplitude, the correlation length, and / or the height profile at a plurality of positions along the direction.

[0192] Referring generally again to Figures 1A to Figure 6 . Each of the steps in any of the various methods can be performed by one or more controllers (such as controller 124 and the like), and the controller can be configured according to any of the embodiments described herein. For example, the method can be performed by any system. The method can also include one or more additional steps that can be performed by the controllers or any system embodiments described herein.

[0193] In some instances, optical scattering-based metrology involves determining the dimensions of a sample by back-solving a predetermined measurement model with measurement data. The back-solving includes, but is not limited to, model-based regression, tomography, machine learning, or any combination thereof. In this way, the target profile parameters are estimated by solving for the values of a parameterized measurement model that minimizes the error between the measured optical intensity and the modeled results.

[0194] As used in this disclosure, the term "sample" generally refers to a substrate formed of semiconductor or non-semiconductor material, which includes one or more "layers" or "films" and a patterned structure that is typically selected to be periodic according to optical metrology. For example, semiconductor or non-semiconductor materials include, but are not limited to, single-crystalline silicon, gallium arsenide, and indium phosphide. The layers formed on the substrate may include, but are not limited to, photoresist, dielectric material, conductive material, or semi-conductive material. Several different types of sample layers are known in the art, and the term sample as used herein is intended to cover the substrate and any type of layer formed thereon. In addition, for the purposes of this disclosure, the terms sample and wafer should be construed as interchangeable. Additionally, for the purposes of this disclosure, the terms patterning device, mask, and reticle should be construed as interchangeable.

[0195] All methods described herein may include storing the results of one or more steps of a method embodiment in a memory. The results may include any of the results described herein and may be stored in any manner known in the art. The memory may include any of the memories described herein or any other suitable storage medium known in the art. After storing the results, the results may be accessed from the memory and used by any of the methods or system embodiments described herein, formatted for display to a user, used by another software module, method, or system, and the like. Additionally, the results may be stored "permanently", "semi-permanently", "temporarily", or for a period of time. For example, the memory may be random access memory (RAM) and the results need not be stored in the memory indefinitely.

[0196] Further contemplated, each of the embodiments of the above methods may include any other steps of any other methods described herein. Additionally, each of the embodiments of the above methods may be performed by any of the systems described herein.

[0197] Those skilled in the art will recognize that the components, operations, devices, objects, and their accompanying discussions described herein are used as examples to clarify the concepts and various configuration modifications may be considered. Thus, as used herein, the specific examples and accompanying discussions set forth are intended to represent their more general classes. In general, the use of any specific example is intended to represent its class, and the omission of specific components, operations, devices, and objects should not be considered limiting.

[0198] As used herein, directional terms such as "top", "bottom", "above", "below", "upper", "upward", "lower", "under", "beneath", and "downward" are intended to provide a relative position for descriptive purposes and are not intended to specify an absolute reference system. Those skilled in the art will appreciate various modifications to the described embodiments, and the general principles defined herein may be applied to other embodiments.

[0199] Regarding the use of substantially any plural and / or singular terms herein, those skilled in the art may convert the plural to the singular and / or the singular to the plural, depending on the context and / or application. For clarity, various singular / plural permutations are not explicitly set forth herein.

[0200] The objects described herein are sometimes shown as different components contained within or connected to other components. It should be understood that such depicted architectures are for illustrative purposes only, and in fact, several other architectures that achieve the same functionality may be implemented. Conceptually, any arrangement of components that achieve the same functionality is effectively "associated" to achieve the desired functionality. Thus, regardless of the architecture or intermediate components, any two components that are combined herein to achieve a particular functionality can be regarded as being "associated" with each other to achieve the desired functionality. Similarly, any two components so associated can also be regarded as being "connected" or "coupled" to each other to achieve the desired functionality, and any two components that can be so associated can also be regarded as being "couplable" to each other to achieve the desired functionality. Specific instances of "couplable" include, but are not limited to, components that can physically mate and / or physically interact and / or can wirelessly interact and / or wirelessly interact and / or logically interact and / or can logically interact.

[0201] In addition, it should be understood that the present disclosure is defined by the appended claims. Those skilled in the art should understand that, generally speaking, the terms used herein and especially in the appended claims (e.g., the body of the appended claims) are generally intended to be "open" terms (e.g., the term "comprising" should be interpreted as "comprising but not limited to", the term "having" should be interpreted as "having at least", etc.). Those skilled in the art should further understand that if a specific number of claim recitations is intended to be introduced, then this intention will be explicitly recited in the claim, and if there is no such recitation, then there is no such intention. For example, as an aid to understanding, the following appended claims may contain the use of introductory phrases such as "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed as implying that the introduction of a claim recitation by the indefinite article "a" limits any particular claim containing such introduced claim recitation to an invention having only one such recitation, even if the same claim contains an introductory phrase such as "one or more" or "at least one" and an indefinite article such as "a" (e.g., "a" should generally be interpreted as meaning "at least one" or "one or more"); the same applies to the use of definite articles for introducing claim recitations. Additionally, even if a specific number of claim recitations being introduced is explicitly recited, those skilled in the art should recognize that such recitation is generally intended to mean at least the recited number (e.g., a bare recitation of "two recitations" without any other modifiers generally means at least two recitations or two or more recitations). Further, in examples where a convention similar to "at least one of A, B, and C and the like" is used, this construction is generally intended to have the meaning commonly understood by those skilled in the art (e.g., a "system having at least one of A, B, and C" will include but not be limited to a system having only A, only B, only C, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). In examples where a convention similar to "at least one of A, B, or C and the like" is used, this construction is generally intended to have the meaning commonly understood by those skilled in the art (e.g., a "system having at least one of A, B, or C" will include but not be limited to a system having only A, only B, only C, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). Those skilled in the art should further understand that, regardless of whether in the detailed description, the claims, or the drawings, almost any disjunctive term and / or phrase presenting two or more alternatives should be understood as contemplating the possibility of including one of the included items, either of the two items, or both items. For example, the phrase "A or B" should be understood as including the possibilities of "A" or "B" or "A and B".

[0202] It is believed that the present disclosure and several attendant advantages thereof will be understood from the foregoing description, and it should be appreciated that various changes may be made in the form, construction, and arrangement of the components without departing from the disclosure or sacrificing all of its material advantages. The described forms are for purposes of illustration only, and the appended claims are intended to cover and embrace such changes. In addition, it is to be understood that the invention is defined by the appended claims.

Claims

1. A inspection system, comprising: A controller, comprising: A memory that maintains program instructions; and One or more processors configured to execute the program instructions to cause the one or more processors to: Generate a geometric model of the structure of a sample; wherein the structure includes a nanosheet profile having surface roughness; wherein the geometric model approximately calculates the surface roughness; Generate an optical response function model of the structure of the sample to illumination based at least in part on the geometric model; wherein the optical response function model simulates the optical response of the nanosheet profile having the surface roughness to the illumination; Receive measurement data from a detector; wherein the measurement data includes a measurement spectrum of the structure detected by the detector; Generate a parametric sub-structure model based at least on the optical response function model and the measurement data; and Extract one or more parameters of the structure based on the measurement data.

2. The inspection system according to claim 1, wherein the geometric model approximately calculates the surface roughness of the nanosheet profile by representing the nanosheet profile as a homogeneous layer and a rough layer; wherein the rough layer is a cladding material surrounding the homogeneous layer.

3. The inspection system according to claim 2, wherein the one or more parameters include the standard deviation of the surface roughness.

4. The inspection system according to claim 2, wherein the homogeneous layer includes a material; wherein the homogeneous layer includes one or more dispersion parameters associated with the material; wherein the one or more dispersion parameters include a refractive index (n) and an extinction coefficient (k).

5. The inspection system according to claim 2, wherein the rough layer includes one or more dispersion parameters determined using an effective medium approximation; wherein the one or more dispersion parameters include a refractive index (n) and an extinction coefficient (k).

6. The inspection system according to claim 5, wherein the rough layer is a mixture of a first material and a second material in a certain ratio; wherein the first material is different from the second material.

7. The inspection system according to claim 6, wherein the ratio is a fixed ratio.

8. The inspection system according to claim 6, wherein the program instructions cause the one or more processors to float the ratio.

9. The inspection system according to claim 5, wherein the rough layer is isotropic; wherein the surface roughness is anisotropic.

10. The inspection system according to claim 1, wherein the geometric model approximately calculates the surface roughness by building blocks; wherein the height of the building blocks varies along a direction.

11. The inspection system according to claim 10, wherein the height of the building blocks is defined by a plurality of segments.

12. The inspection system according to claim 11, wherein each of the plurality of segments includes a segment height at a critical dimension along the direction.

13. The inspection system according to claim 12, wherein the segment height is defined as either a fixed segment height or a percentage segment height.

14. The inspection system according to claim 12, wherein the critical dimension is defined as one of a fixed critical dimension or a percentage critical dimension from the edge.

15. The inspection system according to claim 11, wherein the plurality of segments are plates; wherein the building block includes a stepped shape.

16. The inspection system according to claim 11, wherein the program instructions cause the one or more processors to adjust the resolution of the height of the building block by adjusting the number of the plurality of segments.

17. The inspection system according to claim 10, wherein the height of the building block is defined by one or more polynomial functions.

18. The inspection system according to claim 17, wherein the nanosheet profile includes a first surface and a second surface; wherein the first surface is opposite to the second surface; wherein the first surface is defined by a first polynomial function; wherein the second surface is defined by a second polynomial function; wherein the height of the building block is defined by the first polynomial function and the second polynomial function.

19. The inspection system according to claim 18, wherein the first polynomial function is different from the second polynomial function.

20. The inspection system according to claim 10, wherein the one or more parameters include roughness amplitude and correlation length.

21. The inspection system according to claim 10, wherein the one or more parameters include height profiles at a plurality of positions along the direction.

22. The inspection system according to claim 1, comprising a user input source; wherein the program instructions cause the one or more processors to receive user input from the user input source; wherein the one or more processors generate the geometric model at least partially based on the user input.

23. The inspection system according to claim 1, comprising an optical imaging subsystem; wherein the optical imaging subsystem includes an illumination source and the detector; wherein the illumination source generates the illumination; wherein the detector is communicatively coupled to the controller.

24. The inspection system according to claim 23, wherein the optical imaging subsystem includes at least one of a spectroscopic ellipsometer, a reflectometer, a small-angle x-ray scatterometer, a scanning electron microscope, or a transmission electron microscope.

25. The inspection system according to claim 1, wherein the nanosheet profile includes at least one of a rhombic cross-section, an elliptical cross-section, a triangular cross-section, a rectangular cross-section, or a trapezoidal cross-section.

26. The inspection system according to claim 1, wherein the structure is a gate-all-around (GAA) transistor.

27. The inspection system according to claim 1, wherein the nanosheet profile includes a thickness of 5 nanometers or less.

28. The inspection system according to claim 1, wherein the program instructions cause the one or more processors to generate the optical response function model using rigorous coupled-wave analysis (RCWA).

29. The inspection system according to claim 1, wherein the parametric substructure model is a neural network model trained using the optical response function model and the measurement data.

30. A method, comprising: Generating a geometric model of the structure of a sample; Wherein the structure includes a nanosheet profile having surface roughness; Wherein the geometric model approximately calculates the surface roughness; Generating an optical response function model of the structure of the sample to illumination at least in part based on the geometric model; wherein the optical response function model simulates the optical response of the nanosheet profile having the surface roughness to the illumination; Receiving measurement data from a detector; wherein the measurement data includes a measurement spectrum of the structure detected by the detector; Generating a parametric sub-structure model at least based on the optical response function model and the measurement data; and Extracting one or more parameters of the structure based on the measurement data.

31. The method according to claim 30, wherein the geometric model approximately calculates the surface roughness by representing the nanosheet profile as a homogeneous layer and a rough layer; wherein the rough layer is a coating material surrounding the homogeneous layer.

32. The method according to claim 31, wherein the rough layer includes one or more dispersion parameters determined using an effective medium approximation; wherein the one or more dispersion parameters include a refractive index (n) and an extinction coefficient (k).

33. The method according to claim 32, wherein the rough layer is a mixture of a first material and a second material in a certain ratio; wherein the first material is different from the second material.

34. The method according to claim 32, wherein the rough layer is isotropic; wherein the surface roughness is anisotropic.

35. The method according to claim 30, wherein the geometric model approximately calculates the surface roughness by building blocks; wherein the height of the building blocks varies along a direction.

36. The method according to claim 35, wherein the height of the building blocks is defined by a plurality of segments; wherein Each of the plurality of segments includes a segment height at a critical dimension along the direction.

37. The method according to claim 36, wherein the segment height is defined as one of a fixed segment height or a percentage segment height; wherein the critical dimension is defined as one of a fixed critical dimension or a percentage critical dimension from an edge.

38. The method according to claim 35, wherein the height of the building blocks is defined by one or more polynomial functions.

39. The method according to claim 38, wherein the nanosheet profile includes a first surface and a second surface; wherein the first surface is opposite to the second surface; wherein the first surface is defined by a first polynomial function; wherein the second surface is defined by a second polynomial function; wherein the height of the building blocks is defined by the first polynomial function and the second polynomial function.

40. The method according to claim 30, wherein the one or more parameters include at least one of a standard deviation of the surface roughness, a roughness amplitude, a correlation length, and a height profile.

Images